A new analyzing technique for nonlinear time fractional Cauchy reaction-diffusion model equations
This work aims to propose a new analyzing tool, called the fractional iteration algorithm I for finding numerical solutions of nonlinear time fractional-order Cauchy reaction-diffusion model equations. The key property of the suggested technique is its ability and flexibility to investigate linear a...
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| Vydáno v: | Results in physics Ročník 19; s. 103462 |
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| Hlavní autoři: | , , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Elsevier B.V
01.12.2020
Elsevier |
| Témata: | |
| ISSN: | 2211-3797, 2211-3797 |
| On-line přístup: | Získat plný text |
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| Abstract | This work aims to propose a new analyzing tool, called the fractional iteration algorithm I for finding numerical solutions of nonlinear time fractional-order Cauchy reaction-diffusion model equations. The key property of the suggested technique is its ability and flexibility to investigate linear and nonlinear models conveniently and accurately. The proposed approach can be utilized without the use of any transformation, Adomian polynomials, small perturbation, discretization or linearization. The main feature of the fractional iteration algorithm-I is the improvement of an auxiliary parameter that can ensure a rapid convergence. To check the stability, accuracy and speed of the method, obtained results are compared numerically and graphically with the exact solutions and results available in the latest literature. In addition, numerical results are displayed graphically for various cases of the fractional-order α. These results demonstrate the viability of the proposed technique and show that this technique is exceptionally powerful and suitable for solving fractional PDEs. |
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| AbstractList | This work aims to propose a new analyzing tool, called the fractional iteration algorithm I for finding numerical solutions of nonlinear time fractional-order Cauchy reaction-diffusion model equations. The key property of the suggested technique is its ability and flexibility to investigate linear and nonlinear models conveniently and accurately. The proposed approach can be utilized without the use of any transformation, Adomian polynomials, small perturbation, discretization or linearization. The main feature of the fractional iteration algorithm-I is the improvement of an auxiliary parameter that can ensure a rapid convergence. To check the stability, accuracy and speed of the method, obtained results are compared numerically and graphically with the exact solutions and results available in the latest literature. In addition, numerical results are displayed graphically for various cases of the fractional-order α. These results demonstrate the viability of the proposed technique and show that this technique is exceptionally powerful and suitable for solving fractional PDEs. |
| ArticleNumber | 103462 |
| Author | Khan, Tufail A. Chu, Yu-Ming Ahmad, Hijaz Stanimirović, Predrag S. Ahmad, Imtiaz |
| Author_xml | – sequence: 1 givenname: Hijaz surname: Ahmad fullname: Ahmad, Hijaz organization: Department of Basic Sciences, University of Engineering and Technology Peshawar, Pakistan – sequence: 2 givenname: Tufail A. surname: Khan fullname: Khan, Tufail A. organization: Department of Mathematics, University of Swabi, Swabi, Khyber Pakhtunkhwa, Pakistan – sequence: 3 givenname: Imtiaz surname: Ahmad fullname: Ahmad, Imtiaz organization: Faculty of Science and Mathematics, University of Niš, Višegradska 33, Niš 18000, Serbia – sequence: 4 givenname: Predrag S. surname: Stanimirović fullname: Stanimirović, Predrag S. organization: Department of Mathematics, Huzhou University, Huzhou 313000, China – sequence: 5 givenname: Yu-Ming surname: Chu fullname: Chu, Yu-Ming email: chuyuming@zjhu.edu.cn organization: Department of Mathematics, Huzhou University, Huzhou 313000, China |
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| Keywords | Nonlinear fractional PDE Caputo derivative Cauchy reaction-diffusion equation Fractional iteration algorithm-I |
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| References | Ahmad, Khan (b0170) 2020; 51 Ahmad (b0165) 2019; 2 He (b0225) 2012; 25 Bazighifan, Ahmad, Yao (b0100) 2020; 8 Odibat (b0245) 2010; 51 Nawaz, Ahmad, Ahmad (b0060) 2020 Salkuyeh (b0210) 2008; 56 Atangana, Gómez-Aguilar (b0005) 2018; 114 Khan, Hussain, Ahmad, Ahmad (b0145) 2020 He (b0050) 2020; 17 Ahmad, Khan, Stanimirovic, Ahmad (b0085) 2020 Mokhtari (b0195) 2008; 9 El-Dib (b0040) 2018; 4 Ahmad (b0230) 2018; 9 Ahmad, Seadawy, Khan (b0075) 2019 Caputo (b0125) 1967; 13 He (b0135) 2014; 53 He (b0155) 2007; 207 Ahmad, Seadawy, Khan (b0095) 2020 Thounthong, Khan, Hussain, Ahmad, Kumam (b0080) 2018; 6 Ahmad, Ahsan, Zaheer-ud-Din, Ahmad (b0070) 2019; 7 Ahmad, Ahmad, Thounthong, Chu, Cesarano (b0020) 2020; 12 Hesameddini, Latifizadeh (b0205) 2009; 10 Srivastava, Ahmad, Ahmad, Thounthong, Khan (b0025) 2020 Jumarie (b0120) 2006; 51 Ghaneai, Hosseini (b0250) 2016; 40 Sedighi, Shirazi (b0055) 2013; 227 Ahmad, Seadawy, Khan (b0255) 2020; 177 Ahmad, Khan, Cesarano (b0105) 2019; 8 He (b0035) 2019; 854 Ahmad, Khan, Durur, Ismail, Yokus (b0090) 2020 Saberi-Nadjafi, Tamamgar (b0180) 2008; 56 Ahmad, Khan, Cesarano (b0175) 2019; 8 Yu, He, Garcıa (b0235) 2018 Hamoud, Ghadle (b0010) 2019; 5 Ahmad, Ahsan, Hussain, Kumam, Kumam (b0065) 2019; 11 Ahmad, Khan, Inc, Ahmad, Nisar (b0015) 2020; 59 Herisanu, Marinca (b0200) 2010; 1 Sedighi, Daneshmand (b0045) 2014; 28 Yilmaz, Inc (b0220) 2010; 1 Noor, Mohyud-Din (b0215) 2009; 29 Sedighi, Shirazi (b0030) 2012; 19 He, Wu, Austin (b0160) 2010; 1 Batiha, Noorani, Hashim (b0110) 2008; 36 Wang, Liu (b0260) 2016; 5 Ateş, Yildirim (b0190) 2009; 10 Chun (b0185) 2008; 9 Atangana, Baleanu (b0130) 2016; 20 Atangana, Gómez-Aguilar (b0115) 2018; 34 Podlubny (b0140) 1998 Inokuti, Sekine, Mura (b0240) 1978; 33 He (b0150) 1999; 34 Ahmad (10.1016/j.rinp.2020.103462_b0090) 2020 He (10.1016/j.rinp.2020.103462_b0150) 1999; 34 Odibat (10.1016/j.rinp.2020.103462_b0245) 2010; 51 Batiha (10.1016/j.rinp.2020.103462_b0110) 2008; 36 He (10.1016/j.rinp.2020.103462_b0225) 2012; 25 Khan (10.1016/j.rinp.2020.103462_b0145) 2020 He (10.1016/j.rinp.2020.103462_b0050) 2020; 17 Ghaneai (10.1016/j.rinp.2020.103462_b0250) 2016; 40 He (10.1016/j.rinp.2020.103462_b0135) 2014; 53 Ahmad (10.1016/j.rinp.2020.103462_b0170) 2020; 51 Hesameddini (10.1016/j.rinp.2020.103462_b0205) 2009; 10 Caputo (10.1016/j.rinp.2020.103462_b0125) 1967; 13 Ahmad (10.1016/j.rinp.2020.103462_b0015) 2020; 59 Ahmad (10.1016/j.rinp.2020.103462_b0065) 2019; 11 Salkuyeh (10.1016/j.rinp.2020.103462_b0210) 2008; 56 Podlubny (10.1016/j.rinp.2020.103462_b0140) 1998 Ahmad (10.1016/j.rinp.2020.103462_b0175) 2019; 8 Sedighi (10.1016/j.rinp.2020.103462_b0030) 2012; 19 Sedighi (10.1016/j.rinp.2020.103462_b0045) 2014; 28 Yilmaz (10.1016/j.rinp.2020.103462_b0220) 2010; 1 He (10.1016/j.rinp.2020.103462_b0155) 2007; 207 Ahmad (10.1016/j.rinp.2020.103462_b0105) 2019; 8 Mokhtari (10.1016/j.rinp.2020.103462_b0195) 2008; 9 Yu (10.1016/j.rinp.2020.103462_b0235) 2018 Ahmad (10.1016/j.rinp.2020.103462_b0095) 2020 Jumarie (10.1016/j.rinp.2020.103462_b0120) 2006; 51 Ahmad (10.1016/j.rinp.2020.103462_b0230) 2018; 9 Ahmad (10.1016/j.rinp.2020.103462_b0085) 2020 Inokuti (10.1016/j.rinp.2020.103462_b0240) 1978; 33 He (10.1016/j.rinp.2020.103462_b0035) 2019; 854 Saberi-Nadjafi (10.1016/j.rinp.2020.103462_b0180) 2008; 56 Thounthong (10.1016/j.rinp.2020.103462_b0080) 2018; 6 Atangana (10.1016/j.rinp.2020.103462_b0005) 2018; 114 El-Dib (10.1016/j.rinp.2020.103462_b0040) 2018; 4 Herisanu (10.1016/j.rinp.2020.103462_b0200) 2010; 1 Ahmad (10.1016/j.rinp.2020.103462_b0075) 2019 Ahmad (10.1016/j.rinp.2020.103462_b0165) 2019; 2 Ahmad (10.1016/j.rinp.2020.103462_b0070) 2019; 7 Atangana (10.1016/j.rinp.2020.103462_b0115) 2018; 34 Srivastava (10.1016/j.rinp.2020.103462_b0025) 2020 Sedighi (10.1016/j.rinp.2020.103462_b0055) 2013; 227 Bazighifan (10.1016/j.rinp.2020.103462_b0100) 2020; 8 Ateş (10.1016/j.rinp.2020.103462_b0190) 2009; 10 Noor (10.1016/j.rinp.2020.103462_b0215) 2009; 29 Hamoud (10.1016/j.rinp.2020.103462_b0010) 2019; 5 Wang (10.1016/j.rinp.2020.103462_b0260) 2016; 5 Nawaz (10.1016/j.rinp.2020.103462_b0060) 2020 Atangana (10.1016/j.rinp.2020.103462_b0130) 2016; 20 Ahmad (10.1016/j.rinp.2020.103462_b0255) 2020; 177 Ahmad (10.1016/j.rinp.2020.103462_b0020) 2020; 12 Chun (10.1016/j.rinp.2020.103462_b0185) 2008; 9 He (10.1016/j.rinp.2020.103462_b0160) 2010; 1 |
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